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%I #4 Dec 08 2013 06:23:00
%S 7,14,14,23,46,25,36,113,139,39,54,250,568,364,57,76,530,1964,2639,
%T 849,81,104,1043,6412,16113,10477,1928,112,138,1939,19711,91448,
%U 117318,38240,4281,151,179,3422,56427,494606,1206656,781467,132356,9315,195,227,5802
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays x(i,j) with row sums sum{j*x(i,j), j=1..k+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..n+1} nondecreasing
%C Table starts
%C ...7....14......23........36..........54...........76..........104.........138
%C ..14....46.....113.......250.........530.........1043.........1939........3422
%C ..25...139.....568......1964........6412........19711........56427......150258
%C ..39...364....2639.....16113.......91448.......494606......2508451....11763318
%C ..57...849...10477....117318.....1206656.....11689997....106244229...895749726
%C ..81..1928...38240....781467....15009944....270547199...4578333280.72152875243
%C .112..4281..132356...4826580...173151602...5873283547.187453633375
%C .151..9315..441895..28172630..1874799298.120044822528
%C .195.19741.1419797.156288347.19099723173
%C .247.40967.4391603.832235200
%H R. H. Hardin, <a href="/A233366/b233366.txt">Table of n, a(n) for n = 1..96</a>
%e Some solutions for n=4 k=4
%e ..1..0..0..1..0....0..0..0..1..0....0..0..1..0..0....1..0..0..0..0
%e ..0..1..0..1..0....1..0..0..0..1....0..0..1..1..0....1..1..1..0..0
%e ..0..1..0..0..1....0..1..0..0..1....1..1..0..1..0....0..0..0..1..1
%e ..0..0..1..1..1....0..1..0..0..1....0..0..1..0..1....0..1..1..1..1
%e ..1..1..1..1..1....0..0..1..1..1....0..0..0..1..1....0..1..1..1..1
%Y Column 1 is A232871
%Y Row 1 is A232825
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 08 2013